Push-Connect (Shark Bite style) vs Compression or Sweat Solder

Ok guys, first post here. I was looking around at forums that had active knowledgeable people and this seemed to fit the bill.
I have a small plumbing predicament. Roughly 2 years ago I moved into a town home that was roughly 30 years old.
As to be expected every shut off seized up when trying to remove them... No problem.
At that point I sweated new valves on to every connection at the house, except under my kitchen sink.
It was annoyingly tight under there and I opted to use "push-connect" style valves in place.http://www.lowes.com/pd_4136-143-K2..._product_qty_sales_dollar|1&page=2&facetInfo=
Specifically those...
They essentially work like a "shark bite" style connection.

I have had no issues with leaking or anything but yesterday I replaced my kitchen faucet, i turned the valves off with no issue but much to my surprise
when I went to hook up the hose to the cold valve the entire valve blew off the pipe!
By the time I was able to shut the main off I made a pretty good mess and was pretty upset.
Doing some investigating I found I could push the valve on the pipe and through it would give some resistance I could pull it off the pipe with relative ease
I had a spare valve of the same type when I pushed on and am unable to pull off...
So now I am paranoid, I don't know what failed in the valve or if it will happen again.
I called a few local plumbers just so I wouldn't need to take time off work to repair but all of them are wanting to use compression fittings.
Hell, I am not going to pay someone to put a compression fitting on.

So, finally the question...

Would a compression fitting be a better option than these push-connect style fittings?
Sweating wouldn't be fun in the space I have but it is certainly not impossible, part of me feels like I should give this a shot
but I really don't want to catch my cabinets on fire.

A compression fitting is going to give you a more robust and reliable seal than a sharkbite, regardless of what anyone says.

It is also insanely-easy to install -- slip it on and tighten -- so I'm really unclear why you don't just do that yourself... Do you have a sufficient length of copper pipe coming out of the wall? If so, that would be what I would do. We recommend it all the time. You generally need about an inch of pipe minimum, depending upon the particular valve.

What material is the pipe? Likely copper at that age. Did the pipe have paint on it, or was it clean? A compression fitting requires the pipe to be clean and not all scratched up, which may be the situation after install of the push-on fitting. The actual Sharkbite fitting has a SS toothed ring that is pretty aggressive to hold it on the pipe. The other's likely use similar. If the fitting was not fully seated, that may have been the issue. The instructions on the Sharkbite have you mark the pipe, then, when pushing it on, verify that the end of the fitting made it all the way to the mark. This stabilizes the fitting and ensures it can properly seal and stay there. The ones you have probably have a similar instruction.

Yeah, sorry for the first post being confusing. What I was getting at was there was no way I was going to pay someone to put a compression valve on.
I have copper coming out from the wall, i think there is a little roughing up of the pipe from where the connector bit in but I think that is further back than where a compression fitting would sit.
This particular Keeney valve does not have any instruction regarding how far up the pipe it should go and therefore it is possible it was not seated, but as I stated on that particular valve I couldn't ever
get that valve to stay properly on the pipe after it blew off but an identical new valve would.
I will take another look and see if I can get a torch up there to sweat them on, but if I can't... would it be the general consensus that a tradition compression fitting
would be more reliable than a push-connect style valve? Or would a proper push-connect like a shark bite be a better bet?
I am actually a master technician for FMC so I am more competent than your average weekend warrior DIY'er
but I certainly am not beyond getting good advice from people who have more experience in a field than I do.

When I sweat joints in tight locations, I use shield made from a #10 can with top and bottom removed and split down the seam, and a slot roughly cut 1/2 way up a side and about 1" or so wide. You also need to keep a spray bottle of water at hand just in case.

The metal shields help, and, they make spray flame protection foam you can spray on the wall that helps as well. A 1/2" Sharkbite needs about an inch of pipe to seat fully if I remember (it says on the package and varies by the diameter of the fitting). A compression fitting also needs a moderate amount of pipe, as the pipe goes into the valve, then you have the compression ring and the nut towards the outside. If where the compression fitting will sit is smooth ,it will work. If that area isn't clean, then maybe your best bet is to solder on a valve - the solder will fill in minor scratches fine if you clean it up well and flux it properly.